Experimental confirmation of negative phase change in negative index material planarsamplesD. Vier, D. R. Fredkin, A. Simic, S. Schultz, and Minas Tanielian Citation: Applied Physics Letters 86, 241908 (2005); doi: 10.1063/1.1947903 View online: http://dx.doi.org/10.1063/1.1947903 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/86/24?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Strongly birefringent metamaterials as negative index terahertz wave plates Appl. Phys. Lett. 95, 171104 (2009); 10.1063/1.3253414 Enhanced transmission through a subwavelength aperture using metamaterials Appl. Phys. Lett. 95, 052103 (2009); 10.1063/1.3195074 The influences of substrate and metal properties on the magnetic response of metamaterials at terahertz region J. Appl. Phys. 104, 033505 (2008); 10.1063/1.2961327 Experimental verification of apparent negative refraction in low-epsilon material in the microwave regime J. Appl. Phys. 101, 086103 (2007); 10.1063/1.2424319 Experimental verification of backward-wave radiation from a negative refractive index metamaterial J. Appl. Phys. 92, 5930 (2002); 10.1063/1.1513194

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Experimental confirmation of negative phase change in negative indexmaterial planar samples

D. Vier, D. R. Fredkin, A. Simic, and S. Schultza!

University of California San Diego, 9500 Gilman Dr., La Jolla, California 92093

Minas TanielianBoeing Phantom Works, P.O. Box 3999, Seattle, Washington 98124

sReceived 8 December 2004; accepted 9 May 2005; published online 8 June 2005d

We use far-field range measurements to determine and confirm the negative phase change througha planar negative index material as a function of frequency. The metamaterial is composed of wiresand split ring resonators. At frequencies for which the surface impedanceZ/Z0=1, we determine theindex snd from the measured phase changesrelative to a vacuumd and via numerical simulation. Inaddition to confirming the simulated negative phase change at the frequency wheren=−1, we findgood agreement with prior Snell’s law measurements fromn=−2.5 to −0.5. This illustrates thatmeasuring the phase change of the transmitted signal can be a practical means of identifying theexistence of negative index in planar test samples. ©2005 American Institute of Physics.fDOI: 10.1063/1.1947903g

The discovery that periodic metamaterials comprised ofunit cells, containing metal wires and split ring resonatorssSRRd could be designed to have a microwave frequencyband where the real parts of both the effective permittivitysed and effective permeabilitysmd were simultaneously nega-tive, opened up the new class of materials whose index ofrefraction can be negative.1 In 1968, Veselago2 predicted thatif a material with dually negative permittivity and permeabil-ity could be found it would have totally new electromagneticwave properties, including:sid A negative index of refractionand sii d a phase velocity opposite to the group velocity. Heemphasized that this meant the phase of an electromagneticwave propagating through a properly designed sample wouldaccumulate negatively, i.e., opposite to that which occurs inall traditional materials. Veselago termed that relationship“Left-handed materials”, which are now increasingly calledNIM snegative index materialsd. The first experimental reportconfirming a negative index of refraction used a wedgesample for a classical Snell’s Law experiment andinterpretation.3 The reality of NIM has since been exten-sively confirmed by other groups.4 While these new reportsconfirmed “negative index”, there has been no reports of farfield range measurements of the expected negative phasechange accumulated by a transmitted plane wave propagat-ing through a planar NIM sample.

Figure 1sad is a representation of our measurement sys-tem. A pair ofP-bands12–18 GHzd horns spaced,200 cmapart is used for the source and detection. The samples areplaced between the horns in an aperture in a wall of theabsorber as shown. The measurements of the S parameters asa function of frequency are obtained using an Agilent8722ES vector network analyzer. In Fig. 1sbd, we presentone example of several studies which were made for calibra-tion and verification of the measurements of the phasechange of the transmitted beamsS21d. A series of Teflonsheetsseach 0.25 in. thickd were tightly stacked and placedin the aperture, and the phase change of S21 between source

and detector was measured as a function of total Teflonthickness at a frequency of 10 GHz. We emphasize that whatis plotted in Fig. 1sbd is the phase change at each frequencyrelative to the “no sample” condition. As can be seen, theexperimental points exhibit an excellent agreement with thepredicted phase changefdashed line in Fig. 1sbdg calculatedfrom a simple relationDf=sn−1dk0L wherek0 is the free-space wave vector,n=1.44, andL is the thickness of Teflon.

In Fig. 2, we presentssolid curved the experimental mag-nitude of the transmitted waveuS21u versus frequency from13.5 to 16 GHz for a NIM sample. The samples15 cm

adElectronic mail: sschultz@ucsd.edu

FIG. 1. sad Free-space transmitted phase measurement system andsbd Tefloncalibration data where the theoreticalsdashedd curve is calculated from therelationDf=sn−1dk0L with n=1.44.

APPLIED PHYSICS LETTERS86, 241908s2005d

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314 cm cross sectiond was fabricated as described in5, andis made with a dual SRR and two wires per unit cell. For alldata shown, the sample thickness is 3 unit cellss1 cmd. Thesmooth dashed curve is a result of a numerical S-matrix cal-culation made utilizing Ansoft’sHFSS V8.0software. Exceptfor a slight frequency shift, the experiment and simulationagree well, as shown by the dotted line, which is the simu-lation result shifted by +0.15 GHz. We note that findingsmall frequency shifts between the numerical simulation andthe measured properties for the presently made samples isquite common. We also note for our analysis that follows,that the maximum in S21 is 0.9 indicating that in the regionnear 14.2 GHz the impedance match is very close to 1 fornormal incidence.

In Fig. 3, we plot the raw datasdotted curved exactly aspresented by the Agilent VNA for the phase change of S21referenced to as no samplesi.e., an air pathd. The phasechange of S21 as measured by the Agilent VNA or otherwisedetermined via simulations, is only defined modulo 360°.Thus, any 360° phase discontinuity should be corrected. InFig. 3 sdotted curved, the discontinuity at 13.7 GHz can beremoved by a 360° adjustment of the data points on eitherside. However, the phase change data can still be off by

another integer multiple of 360°. We emphasize two key pre-mises for being able to correctly assign these 360° correc-tions without the need for any additional experimental infor-mation: sid The frequency–phase change data underconsideration always lie within the first Brillouin zonescor-responding to the lowest NIM passband mode of the systemdso the phase shift of one unit cell is between ±180°, andsii dthere are appropriate numerical simulation data available toconfirm the magnitude of the expected phase change for oneunit cell at a frequency near the conditionZ/Z0,1, n,−1.In our HFSS simulation, we confirmed that these two condi-tions, as designed, occurred at a frequency of 14 GHz. Sinceour unit cell was 3.33 mm, a phase shift of,u56°u occurs forthe wave traveling in either then= +1 or n=−1 state. Thephase change for the NIM samplesrelative to no sampledwhen n=−1 is given by twice this number or,−112° percell. For three cells, this amounts to,−336°. We confirmedthat after applying a 360° correction, ourHFSSsimulation ofa three-cell sample correctly corresponded to the phasechange as shown in Fig. 3sdashed curved, and then appliedthe same correction to the experimental phase change data,resulting in the solid curve of Fig. 3.sTo avoid confusion, wedo not make the 0.15 GHz frequency shift that was illus-trated in Fig. 2.d We do emphasize at this point that thealgebraic sign of the experimental phase changesand simu-lationd correspond to negative values as expected.6

In Fig. 4, we present the refractive indexn versus fre-quency determined in three ways:s1d sSolid curved, n is de-termined using the experimental phase difference data of Fig.3 from the relationDf=sn−1dk0L, s2d sdashed curved n isdetermined from the full numerical simulation S-matrix viathe retrieval method of5, and s3d sblack diamondsd n is ex-perimentally measured via Snell’s law experiments on a12° wedge sample.5 It is clear that if one does apply a 0.15GHz shift to the simulation data, then over the index rangefrom −2.5 to −0.5, there is a quite satisfactory agreement forall three data sets.

From the agreement between the three data sets pre-sented in Fig. 4, we conclude that we have confirmed theaccumulation of a negative phase change for a NIM samplein the frequency range of 13.6–14.6 GHz. We note that whilethe full S-matrix numerical simulation correctly displays a

FIG. 2. uS21u vs frequency for experimental datassolid curved, simulationdatasdashed curved, and simulation data shifted by 0.15 GHzsdotted curved.

FIG. 3. Phase change of S21 vs frequencysad raw experimental datasdottedcurved, sbd experimental data with 360 ° correctionsssolid curved, and scdsimulation data with 360 ° correctionssdashed curved.

FIG. 4. Refractive indexn vs frequencysad calculated from measured phasessolid curved, sbd from full numerical simulation of the S matrixsdashedcurved, andscd measured in the wedge experiment5 sblack diamondsd.

241908-2 Vier et al. Appl. Phys. Lett. 86, 241908 ~2005!

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kink nearn=0 at 14.75 GHzsindicating the upper edge ofthe negative index bandd, our deduced values ofn from thephase data do not. The simple expressionDf=sn−1dk0L isno longer qualitatively valid for then,0 region, or fornmore negative that −2.5 as the sample is far from matched inthose regions. Despite this limitation, we suggest that thecareful determination of the correct phase change throughtest samples via the analysis illustrated herein, and in thefrequency region where the surface impedance is closelymatched to free space, is a rigorous test for confirmation ofthe negative index property without the need for a wedgesample. Because it is a far field range measurement, the tech-nique can be applied at arbitrarily high frequencies, wherethe possibility of making phase measurements within thesample7 is no longer practical.

The authors thank Matt Schuerman for his help with thephase measurements. They also thank Dr. Valerie Browning

for her encouragement in the importance of performingrange measurements as confirmation of the negative phasechange property of NIM. This work was supported by GrantNos. DARPA/AFOSR MDA972-01-2-0016 and DOE-DE-FG-03-01ER45881.

1D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz,Phys. Rev. Lett.84, 4184s2000d.

2V. G. Veselago, Sov. Phys. Usp.10, 509 s1968d.3R. A. Shelby, D. R. Smith, and S. Schultz, Science292, 77 s2001d.4Science302 2043s2003d; the editors of this issue chose the confirmationof NIM as one of the top ten breakthroughs of 2003. References are citedtherein.

5R. B. Greegor, C. G. Parazzoli, C. K. Li, B. E. C. Koltenbah, and M.Tanielian, Opt. Express11, 688 s2003d.

6Using HFSS, we have also performed eigenmode calculations and deter-mined the lowest pass-band of the NIM-band structure whose dispersionyields an index–frequency relation in agreement with the full S-matrixsimulation of Fig. 4.

7S. A. Cummer and B.-I. Popa, Appl. Phys. Lett.85, 4564s2004d.

241908-3 Vier et al. Appl. Phys. Lett. 86, 241908 ~2005!

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